{"questions":[{"uuid":"3cdc564f-7f2b-49bc-86a2-4a57b82adedf","question":"Solve the system of equations:

2x + y = 10

and

x - y = 1

.","answer":"(3, 4)","alternatives":["(5, 0)","(2, 6)","(4, 2)"],"answerExplanation":"By adding the equations:

(2x + y) + (x - y) = 10 + 1

, we get

3x = 11

, so

x = 3

. Substituting

x

back into the second equation:

3 - y = 1

gives

y = 2

. So, the solution is

(3, 2)

.","hint":"Try adding the equations to eliminate

y

.","imageEnabled":false,"duration":30,"latexEnabled":false,"audioEnabled":false,"htmlEnabled":true,"questionId":"3cdc564f-7f2b-49bc-86a2-4a57b82adedf"},{"uuid":"833d4b6a-1942-4f03-84c0-5479c6e6beea","question":"Solve the system of equations:

3x + 2y = 12

and

2x - 2y = 4

.","answer":"(4, 0)","alternatives":["(0, 6)","(2, 3)","(5, 1)"],"answerExplanation":"Adding the equations

(3x + 2y) + (2x - 2y) = 12 + 4

eliminates

y

, giving

5x = 16

, so

x = 4

. Substituting

x

back into

3x + 2y = 12

results in

12 + 2y = 12

, leading to

2y = 0

, thus

y = 0

.","hint":"Consider eliminating

y

by adding the equations.","imageEnabled":false,"duration":30,"latexEnabled":false,"audioEnabled":false,"htmlEnabled":true,"questionId":"833d4b6a-1942-4f03-84c0-5479c6e6beea"}]}

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